2.5 subgroup - Revision history

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2026-10-21T06:25:30Z

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← Older revision		Revision as of 06:25, 21 October 2026
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	The 2.5 subgroup is a [[retraction]] of the [[5-limit]], obtained by removing prime 3. Its simplest [[expansion]] is the [[2.5.7 subgroup]], which adds prime [[7/1\|7]].		The 2.5 subgroup is a [[retraction]] of the [[5-limit]], obtained by removing prime 3. Its simplest [[expansion]] is the [[2.5.7 subgroup]], which adds prime [[7/1\|7]].

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	[[Category:Rank-2 temperaments]]		{{Stub}}
			[[Category:Just intonation subgroups\|#]]
			[[Category:Rank-2 temperaments\|#]]
			[[Category:5-limit\|#]]

CompactStar at 00:32, 21 October 2026

2026-10-21T00:32:17Z

← Older revision		Revision as of 00:32, 21 October 2026
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	The '''2.5 subgroup''' is [[just intonation subgroup]] consisting of [[rational interval]]s where 2 and 5 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 2 and 5. This is an infinite set. Some examples of intervals in this subgroup are [[5/4]], [[8/5]], [[25/16]], [[32/25]], and so on.		The '''2.5 subgroup''' is [[just intonation subgroup]] consisting of [[rational interval]]s where 2 and 5 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 2 and 5. This is an infinite set. Some examples of intervals in this subgroup are [[5/4]], [[8/5]], [[25/16]], [[32/25]], and so on.

			The 2.5 subgroup is a [[retraction]] of the [[5-limit]], obtained by removing prime 3. Its simplest [[expansion]] is the [[2.5.7 subgroup]], which adds prime [[7/1\|7]].

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			[[Category:Rank-2 temperaments]]

CompactStar: Created page with "The '''2.5 subgroup''' is just intonation subgroup consisting of rational intervals where 2 and 5 are the only allowable prime factors, so that every such interval may be written as a ratio of integers which are products of 2 and 5. This is an infinite set. Some examples of intervals in this subgroup are 5/4, 8/5, 25/16, 32/25, and so on. {{stub}}"

2026-10-21T00:30:41Z

Created page with "The '''2.5 subgroup''' is just intonation subgroup consisting of rational intervals where 2 and 5 are the only allowable prime factors, so that every such interval may be written as a ratio of integers which are products of 2 and 5. This is an infinite set. Some examples of intervals in this subgroup are 5/4, 8/5, 25/16, 32/25, and so on. {{stub}}"

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The '''2.5 subgroup''' is [[just intonation subgroup]] consisting of [[rational interval]]s where 2 and 5 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 2 and 5. This is an infinite set. Some examples of intervals in this subgroup are [[5/4]], [[8/5]], [[25/16]], [[32/25]], and so on.
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